Problem: What is the extraneous solution to these equations? $\dfrac{x^2 + 10}{x + 4} = \dfrac{26}{x + 4}$
Answer: Multiply both sides by $x + 4$ $ \dfrac{x^2 + 10}{x + 4} (x + 4) = \dfrac{26}{x + 4} (x + 4)$ $ x^2 + 10 = 26$ Subtract $26$ from both sides: $ x^2 + 10 - (26) = 26 - (26)$ $ x^2 + 10 - 26 = 0$ $ x^2 - 16 = 0$ Factor the expression: $ (x - 4)(x + 4) = 0$ Therefore $x = 4$ or $x = -4$ At $x = -4$ , the denominator of the original expression is 0. Since the expression is undefined at $x = -4$, it is an extraneous solution.